Premium
A strong maximum principle for weak solutions of quasi‐linear elliptic equations with applications to Lorentzian and Riemannian geometry
Author(s) -
Andersson Lars,
Galloway Gregory J.,
Howard Ralph
Publication year - 1998
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199806)51:6<581::aid-cpa2>3.0.co;2-3
Subject(s) - mathematics , maximum principle , mathematical analysis , manifold (fluid mechanics) , curvature , sectional curvature , space (punctuation) , riemannian manifold , class (philosophy) , elliptic curve , product (mathematics) , pure mathematics , geometry , scalar curvature , optimal control , mathematical optimization , mechanical engineering , linguistics , philosophy , artificial intelligence , computer science , engineering
The strong maximum principle is proved to hold for weak (in the sense of support functions) sub‐ and supersolutions to a class of quasi‐linear elliptic equations that includes the mean curvature equation for C 0 ‐space‐like hypersurfaces in a Lorentzian manifold. As one application, a Lorentzian warped product splitting theorem is given. © 1998 John Wiley & Sons, Inc.